Gamma Gaussian inverse Wishart cardinalized probability hypothesis density (GGIW-CPHD) algorithm was always used to track group targets in the presence of cluttered measurements and missing detections. A multiple models GGIW-CPHD algorithm based on best-fitting Gaussian approximation method (BFG) and strong tracking filter (STF) is proposed aiming at the defect that the tracking error of GGIW-CPHD algorithm will increase when the group targets are maneuvering. The best-fitting Gaussian approximation method is proposed to implement the fusion of multiple models using the strong tracking filter to correct the predicted covariance matrix of the GGIW component. The corresponding likelihood functions are deduced to update the probability of multiple tracking models. From the simulation results we can see that the proposed tracking algorithm MM-GGIW-CPHD can effectively deal with the combination/spawning of groups and the tracking error of group targets in the maneuvering stage is decreased.